As a second possibility, we assume that the FC knows only that the number of Byzantines is lower than \(n/2\) . As already observed in previous works [1]}, [2]}, [3]}, and as it is easily arguable, when the number of Byzantines exceeds the number of honest nodes no meaningful decision can be made. Then it makes sense for the FC to assume that \(N_B < n/2\) , since if this is not the case, no correct decision can be made anyhow. Under this assumption, the maximum entropy distribution is the one which assigns exactly the same probability to all the sequences \(a^n\)  for which \(\sum _i a_i < n/2\) . To derive the optimum decision fusion strategy in this setting, let \(\mathcal {I}\)  be the indexing set \(\lbrace 1,2,...,n\rbrace \) . We denote with \(\mathcal {I}_k\)  the set of all the possible \(k\) -subsets of \(\mathcal {I}\) . Let \(I \in \mathcal {I}_k\)  be a random variable with the indexes of the byzantine nodes, a node \(i\)  being byzantine if \(i \in I\) , honest otherwise. We this notation, we can rewrite (REF ) as
\(s^{m,*} = \arg \max _{s^m} \sum _{k=0}^{\lfloor n/2 \rfloor }\sum _{I \in \mathcal {I}_{k}} P({\bf r} | I, s^m ) p(s^m),\) 
